Working in a less heated market with more available properties to choose from I might have backed from the deal but over all house is in good shape and have great potential for improvement and cash flow. 

I'd sell the property in the spring when things heat up.

sounded like probably something that got heated on both ends..

As an example, she likes to use the stove to heat her unit instead of the wall heater which is fully functional despite being told repeatedly that she shouldn't do that.

We have a heat vent coming out of the cabinet below our sink. 

The past six weeks the heat in my apartment has been erratic, sometimes with the furnace just not working.

For HVAC, I think split type of A/C unit should be fine for both cooling and heating for 700sf space, run by electricity, given the mild CA bay area's weather.   

Here are some of the options we are considering:1) Keep the system basically as is, but update it for greater energy efficiency. - Install two new high efficiency condensing boilers, and update windows and insulation for better heat loss performance.PROS - a) minimally invasive; b) can provide 15-30% reduction in heating costs (we are told).CONS - a)total gas expense is still paid by the landlord; b) individual units won't have individual control (except for a thermostat controlled shutoff valve for heat/water in each unit); c) AC would be available on with in wall/window units. 2) Try to individually meter each units' gas and provide each with a traditional forced air heating/cooling system.PROS: a)gas expense could be completely removed for landlord (huge)- even tankless hot water could be installed in each unit; b) each unit would have their own climate control.CONS: a) constructions costs of running new gas lines and soffiting sheet metal duct work. b) highly invasive with collateral construction costs; c) future costs of maintenance on multiple systems vs a single building-wide system. 3) An electric based heating system- This is tricky in my mind because of the high cost of electric heat.

Come to think of it, I have a rental with an oil tank for heat.

One of the cons here is that current owner pays utilities (water, sewer, trash, heat... waiting on electricity #) which average to about $421/mo.